Difference between revisions of "Evolvent"
From Encyclopedia of Mathematics
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An evolvent is a region in the plane that is isometric to a given region on a developable surface. Example: The evolvent of the side surface of a cone cut along a generator is a planar sector. The approximate construction of an evolvent can be achieved graphically by means of descriptive geometry. | An evolvent is a region in the plane that is isometric to a given region on a developable surface. Example: The evolvent of the side surface of a cone cut along a generator is a planar sector. The approximate construction of an evolvent can be achieved graphically by means of descriptive geometry. | ||
| − | The evolvent of a polyhedral surface is a set of polygons (the faces of the evolvent) with a rule for glueing their sides that defines a [[ | + | The evolvent of a polyhedral surface is a set of polygons (the faces of the evolvent) with a rule for glueing their sides that defines a [[polyhedral metric]] isometric to the internal geometry of the polyhedral surface. The faces of the evolvent need not coincide with the real faces of the surface: when laid on the surface they may be folded. |
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====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , Springer (1973)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , Springer (1973)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 15:03, 10 April 2023
An evolvent is a region in the plane that is isometric to a given region on a developable surface. Example: The evolvent of the side surface of a cone cut along a generator is a planar sector. The approximate construction of an evolvent can be achieved graphically by means of descriptive geometry.
The evolvent of a polyhedral surface is a set of polygons (the faces of the evolvent) with a rule for glueing their sides that defines a polyhedral metric isometric to the internal geometry of the polyhedral surface. The faces of the evolvent need not coincide with the real faces of the surface: when laid on the surface they may be folded.
References
| [a1] | W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , Springer (1973) |
How to Cite This Entry:
Evolvent. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Evolvent&oldid=53748
Evolvent. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Evolvent&oldid=53748
This article was adapted from an original article by V.A. Zalgaller (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article